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C4 Parametric equations

I cant answer this question.. I'm not sure how to rearrange it to cancel out t...


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(edited 7 years ago)
Original post by zayn008
I cant answer this question.. I'm not sure how to rearrange it to cancel out t...




What have you tried?
Original post by zayn008
I cant answer this question.. I'm not sure how to rearrange it to cancel out t...


Attachment not found


Substitute x in terms of t and y in terms of t into the Cartesian equation and show it equals 4.

As far as exam technique goes, you should sort of get a hint about doing this because the question asks you to 'verify'
(edited 7 years ago)
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Original post by RDKGames
What have you tried?


So far ive tried rearranging to get x = ... but cant seem to do that without having a t on one side, ive also tried putting x into the Cartesian equation to prove it gives y which got me up to y^2 + t^2 - 1/(t^2) = 2
Original post by zayn008
So far ive tried rearranging to get x = ... but cant seem to do that without having a t on one side, ive also tried putting x into the Cartesian equation to prove it gives y which got me up to y^2 + t^2 - 1/(t^2) = 2


If you'd like to obtain the Cartesian equation directly, then try squaring both parametric forms of x and y. See if you can notice anything you can do from there to remove dependency on t.
Original post by zayn008
So far ive tried rearranging to get x = ... but cant seem to do that without having a t on one side, ive also tried putting x into the Cartesian equation to prove it gives y which got me up to y^2 + t^2 - 1/(t^2) = 2


By substituting for xx and yy you get

(t+t−1)2−(t−t−1)2⇒(t2+2+t−2)−(t2−2+t−2)(t+t^{-1})^2-(t-t^{-1})^2 \Rightarrow (t^2+2+t^{-2})-(t^2-2+t^{-2}) and show that it equals 4.
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Original post by crashMATHS
If you'd like to obtain the Cartesian equation directly, then try squaring both parametric forms of x and y. See if you can notice anything you can do from there to remove dependency on t.


I tried what you mentioned above and got 4, so i guess that works. Everything just cancelled out to give 4... 30 minutes of algebra and it was that simple :colonhash:

It seems too complex, i think that's why they've just given the equation beforehand

Thanks! :wink:
Original post by zayn008
I tried what you mentioned above and got 4, so i guess that works. Everything just cancelled out to give 4... 30 minutes of algebra and it was that simple :colonhash:

It seems too complex, i think that's why they've just given the equation beforehand

Thanks! :wink:


They key word there is 'verify' which hints you to simply substitute some thing into another and show that the relation of that other thing remains as proposed. It's why it's only 2 marks - all you're doing is substituting one thing into another.

I.e. Substitute the parametric equations into the Cartesian equation and show that it equals 4 proposed in the context

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